Nielsen, 38, is head coach at the Centre of Excellence in Brisbane, which includes managing the respected Australian Institute of Sport (AIS) men's cricket programme.
He took over that role in 2005 after spending three years assisting Buchanan in the coaching of the Australian team.
Nielsen, a former wicketkeeper-batsman for South Australia, will begin work in his new role after the World Cup, Cricket Australia said.
Nielsen was appointed a week after former Australian Test player Tom Moody, the highly regarded coach of Sri Lanka, announced he was not interested in the position.
"I'm incredibly proud, honoured and excited to have been offered this opportunity," Nielsen said in a statement.
"Moving forward, this job represents a great opportunity to work with a fine group of players who are an excellent cricket team.
"Over the coming period there will be some transition in the playing group and I look forward to working with the exciting emerging talent in this country as we